The blasts came after French president Francois Hollande said the country's forces had attained their objectives in Mali

Timbuktu has been hit by a prolonged battle between Islamic extremists and the Malian and French armies, residents and a Malian military spokesman has said.

Fighters linked to al Qaeda in the Islamic Maghreb, or AQIM, attacked the city in northern Mali late on Saturday night and have continued fighting on Sunday, said Captain Samba Coulibaly, spokesman for the Malian military in Timbuktu.

The attack started when a jihadist suicide bomber blew himself up at a Malian military checkpoint at the western entrance to Timbuktu, he said. "The jihadist was on foot and died on the spot, but his explosives lightly injured one of our soldiers," said Capt Coulibaly.

"The jihadists are a few. They sneaked into the military camp and the city of Timbuktu. There is shooting at the moment, but we'll get to the end," said a Malian soldier at an entrance to the city.

The French military joined the Malian army to fight the Islamic radicals, said Timbuktu residents. On Sunday afternoon, shooting could still be heard in the city, said resident Age Djitteye. He said that one of the jihadists tried to take cover inside his family's compound: "He was young. He was wearing a robe, and had ammunition belts across his chest and a turban. He came inside our compound, and then the French came. He ran and they chased him."

Mr Djitteye said a suicide bomber blew himself up on one of the only paved roads at the heart of Timbuktu, close to the Hotel Colombe, the town's main hotel used by journalists and aid workers.

In a separate incident, a Malian army vehicle drove over a land mine during a patrol Saturday around 70 miles from the northern Malian town of Ansongo, killing two people on board, said the Malian military.

The attacks come as French President Francois Hollande said on French television on Saturday that French forces had attained their objectives in Mali, a country which until January had lost its northern half to an al Qaida cell and their allies.

When the extremists began advancing southward in early 2013, Mr Hollande unilaterally authorised a military intervention which quickly pushed the Islamic extremists from the main cities in Mali's north. Outside the heavily fortified cities like Timbuktu, however, the jihadists are still present, leading an insurgency marked by suicide bombings, land mines and attacks on the cities.

For 10 months until this January, Timbuktu and much of the rest of northern Mali was ruled by al Qaida in the Islamic Maghreb, as well as two other jihadist groups allied with the terror network.